Module Algebra Structures of Non-Standard Quantum Group Xq(A1) on <semantics>C</semantics>[x,y,z] - Dong Su (Mathematics)
In this paper, we investigate the module algebra structures of <semantics>Xq(A1)</semantics> on the quantum polynomial algebra <semantics>Cq[x,y,z]</semantics>. The automorphism group of <semantics>Cq[x,y,z]</semantics> is denoted by <semantics>Aut(Cq[x,y,z])</semantics>, and we give a complete classification of <semantics>Xq(A1)</semantics>-module algebra structures on <semantics>Cq[x,y,z]</semantics>, where <semantics>K1,K2∈Aut(Cq[x,y,z])</semantics>.